HP 12C Calculator: Loan Calculations and Solutions, Notas de estudo de Engenharia Mecânica

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HP 12C Basic loan calculations

Loan calculations

The HP12C TVM

Cash flow diagrams and sign conventions

Practice solving loan problems

HP 12C Basic loan calculations

Loan calculations

A loan is an agreement between two parties where one party borrows money and agrees to pay back to the other party (often a financial institution) over a set period of time with interest. The amount of money that is borrowed is called the principal and the interest is the payment for borrowing the money. The time set to pay back the loan is known as the term. Loan calculations are annuity problems involving TVM (time value of money) calculations involving the concepts of the present value of money ( PV ), future value of money ( FV ), periodic payments ( PMT ), interest rates ( i ), and number of periods ( n ).

The HP12C TVM

Standard HP12C features solve these types of problems with the five TVM keys n, ¼, $, P and M. These keys are associated to the five TVM registers n, i, PV, PMT and FV. To set any of these registers to a known value, calculate or key it in and press the corresponding key. Enter each of the four known TVM values, press its related key, then press the key that represents the unknown, fifth value to calculate it.

There are also two functions meant to be an aid when entering or retrieving annual values for n and ¼ : A and C. Pressing gA is the same as pressing \12 μ n, meaning the number of years can be keyed in and stored as number of months automatically. Pressing gC is the same as pressing \12 z ¼, meaning the yearly interest rate can be keyed in and stored as monthly interest rate automatically. It is also possible to retrieve the yearly-related values by pressing :gA (number of years) and/or :gC (yearly interest rate) whenever necessary.

Cash flow diagrams and sign conventions

The sign conventions for cash flows in the HP12C follow this simple rule: money received is positive (arrow pointing up), money paid out is negative (arrow pointing down). The key is keeping the same viewpoint through each complete calculation. The regular use of cash flow diagrams allows a faster approach to solve most TVM-related problems. The cash flow diagram below represents the borrower viewpoint of the most common mortgage problems with balloon payment and their relation to the TVM variables.

Figure 1

$ = Loan amount

P = Monthly payments^ M^ = 0 (typical)

...

n = number of months

(^1 2 3) n-2 n-1 n

¼ = Monthly interest rate

Practice solving loan problems

Example 1: To help sell used cars, a car dealer offers loans with a 10.5% annual percent rate compounded monthly with terms up to 4 years on vehicles from $7,000 to $9,000. Jim wants to buy his dream $8,000 car and wants to know how much will he pay monthly in a 3-year plan.

HP 12C Basic loan calculations

Solution: Set the new n and calculate FV:

29 n M

Figure 4

This means that 29 actual payments of $490 would actually overpay the loan by $44.82. To calculate the actual amount to be paid in the 29th^ payment, simply add the value in the display to the payment amount already available in PMT:

:P +

Figure 5

Answer: The 29th^ payment will be $445.18.